{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QJNBJ6QJPLCM3SYE2UVXDMBIHJ","short_pith_number":"pith:QJNBJ6QJ","canonical_record":{"source":{"id":"1612.01916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-06T17:16:40Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"9048a7e6d2bfe348140ef3f9b198f8b7924669a6de38bc12501c4f0b3b758cb4","abstract_canon_sha256":"ae6566af8f86b0a20c2b6927b2ed148f14abca1a6c15d0a4d6990cdf3b7f67e5"},"schema_version":"1.0"},"canonical_sha256":"825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759","source":{"kind":"arxiv","id":"1612.01916","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01916","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01916v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01916","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"QJNBJ6QJPLCM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJNBJ6QJPLCM3SYE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJNBJ6QJ","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QJNBJ6QJPLCM3SYE2UVXDMBIHJ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.01916","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-06T17:16:40Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"9048a7e6d2bfe348140ef3f9b198f8b7924669a6de38bc12501c4f0b3b758cb4","abstract_canon_sha256":"ae6566af8f86b0a20c2b6927b2ed148f14abca1a6c15d0a4d6990cdf3b7f67e5"},"schema_version":"1.0"},"canonical_sha256":"825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:47.364081Z","signature_b64":"sre9hXWGd3wNLFanc3iWG5tK+Gtseqy4w4NEHwaTiaNrSl1ehK/euhhKzrtWxIj8BzOS3ZjCK7/3NMlLT3pACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759","last_reissued_at":"2026-05-18T00:55:47.363563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:47.363563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.01916","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXFdyxhJ2+12hsRrT7c4VZxWd9h1CkrrFxW2PKpuPjcT6q1RsSDj1+AAQoyowR2mFIfgBP4tKmKSaDEXp3d0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:56:35.347030Z"},"content_sha256":"68accffda138f863d384e2e265094e12dbf4c3c948be6517d61f82890b115eec","schema_version":"1.0","event_id":"sha256:68accffda138f863d384e2e265094e12dbf4c3c948be6517d61f82890b115eec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QJNBJ6QJPLCM3SYE2UVXDMBIHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Dries Stivigny, Manuela Girotti, Tom Claeys","submitted_at":"2016-12-06T17:16:40Z","abstract_excerpt":"We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer $G$-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a $2\\times 2$ Riemann-Hilbert problem, and use this repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01916","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vb2z0Kl0KbBs89U4un/+XNa9XUjrxcNSwJUsO4WcoTqZX9VLSbZxT1ebuw9kGY7p8dndDgIFwPjJiB7HnQ8CBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:56:35.347499Z"},"content_sha256":"339f79617ea5bf8a3748b679ce9de30e3e1e7bd13dd9e083af7fe84a8c735a83","schema_version":"1.0","event_id":"sha256:339f79617ea5bf8a3748b679ce9de30e3e1e7bd13dd9e083af7fe84a8c735a83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/bundle.json","state_url":"https://pith.science/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T10:56:35Z","links":{"resolver":"https://pith.science/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ","bundle":"https://pith.science/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/bundle.json","state":"https://pith.science/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJNBJ6QJPLCM3SYE2UVXDMBIHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QJNBJ6QJPLCM3SYE2UVXDMBIHJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae6566af8f86b0a20c2b6927b2ed148f14abca1a6c15d0a4d6990cdf3b7f67e5","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-06T17:16:40Z","title_canon_sha256":"9048a7e6d2bfe348140ef3f9b198f8b7924669a6de38bc12501c4f0b3b758cb4"},"schema_version":"1.0","source":{"id":"1612.01916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01916","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01916v1","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01916","created_at":"2026-05-18T00:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"QJNBJ6QJPLCM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJNBJ6QJPLCM3SYE","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJNBJ6QJ","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:339f79617ea5bf8a3748b679ce9de30e3e1e7bd13dd9e083af7fe84a8c735a83","target":"graph","created_at":"2026-05-18T00:55:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer $G$-functions or Wright's generalized Bessel functions. They generalize in a natural way the hard edge Bessel kernel Fredholm determinant. We express the logarithmic derivatives of the Fredholm determinants identically in terms of a $2\\times 2$ Riemann-Hilbert problem, and use this repre","authors_text":"Dries Stivigny, Manuela Girotti, Tom Claeys","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-06T17:16:40Z","title":"Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01916","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:68accffda138f863d384e2e265094e12dbf4c3c948be6517d61f82890b115eec","target":"record","created_at":"2026-05-18T00:55:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae6566af8f86b0a20c2b6927b2ed148f14abca1a6c15d0a4d6990cdf3b7f67e5","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-06T17:16:40Z","title_canon_sha256":"9048a7e6d2bfe348140ef3f9b198f8b7924669a6de38bc12501c4f0b3b758cb4"},"schema_version":"1.0","source":{"id":"1612.01916","kind":"arxiv","version":1}},"canonical_sha256":"825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"825a14fa097ac4cdcb04d52b71b0283a6f91bcf35eb8ec9b3e89de4fef19f759","first_computed_at":"2026-05-18T00:55:47.363563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:47.363563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sre9hXWGd3wNLFanc3iWG5tK+Gtseqy4w4NEHwaTiaNrSl1ehK/euhhKzrtWxIj8BzOS3ZjCK7/3NMlLT3pACg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:47.364081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68accffda138f863d384e2e265094e12dbf4c3c948be6517d61f82890b115eec","sha256:339f79617ea5bf8a3748b679ce9de30e3e1e7bd13dd9e083af7fe84a8c735a83"],"state_sha256":"a3217af5aa9496bd7dd97f93d6236e4c3b00cbea9f598b389b02c71b75f48a0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mph6lFyOpXACZ8xjOtV2mM9lYwImCu16nQT3FPWQ44bhMB6VnhZiKVuPx2WExXTVFzPkP+4rNlRoZT1++JwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:56:35.351169Z","bundle_sha256":"26c9db61420156b308b91cfab3ab9c92ba60deef752f98c4c1789b6fe29c5592"}}